Ultrasound directed self-assembly (DSA) utilizes the acoustic radiation force (ARF) associated with a standing ultrasound wave to organize particles dispersed in a fluid medium into specific patterns. The ARF is a superposition of the primary acoustic radiation force, which results from the incident standing ultrasound wave, and the acoustic interaction force, which originates from single and multiple scattering between neighboring particles. In contrast with most reports in the literature that neglect multiple scattering when calculating the ARF, we demonstrate that the deviation between considering single or multiple scattering may reach up to 100%, depending on the ultrasound DSA process parameters and material properties. We evaluate a theoretical case with three spherical particles in a viscous medium and derive operating maps that quantify the deviation between both scattering approaches as a function of the ultrasound DSA process parameters. Then, we study a realistic system with hundreds of particles dispersed in a viscous medium, and show that the deviation between the ARF resulting from single and multiple scattering increases with decreasing particle size and increasing medium viscosity, density ratio, compressibility ratio, and particle volume fraction. This work provides a quantitative basis for determining whether to consider single or multiple scattering in ultrasound DSA simulations.

中文翻译：

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考虑单次和多次散射计算驻超声波场中球形颗粒的声辐射力

超声定向自组装 (DSA) 利用与驻波超声波相关的声辐射力 (ARF) 将分散在流体介质中的颗粒组织成特定的图案。 ARF 是由入射驻超声波产生的初级声辐射力和源自相邻粒子之间的单次和多次散射的声相互作用力的叠加。与大多数文献中在计算 ARF 时忽略多重散射的报道相反，我们证明考虑单一或多重散射之间的偏差可能高达 100%，具体取决于超声 DSA 工艺参数和材料特性。我们评估了粘性介质中三个球形颗粒的理论情况，并得出了操作图，该操作图将两种散射方法之间的偏差量化为超声 DSA 过程参数的函数。然后，我们研究了一个具有数百个颗粒分散在粘性介质中的现实系统，并表明单次和多次散射产生的 ARF 之间的偏差随着颗粒尺寸的减小和介质粘度、密度比、压缩比和颗粒体积的增加而增加分数。这项工作为确定在超声 DSA 模拟中考虑单次散射还是多次散射提供了定量基础。